The linear guides available on the market for medical devices of the kind described at the outset are usually constructed such that the balls are embedded in corresponding ball holders in the form of bores of a bearing or ball cage, hereinafter also referred to only as bearing cage. In particular, moving the machine element back and forth at a high oscillation frequency is a problem with such medical devices. The bearing cage is moved with it with an oscillating movement back and forth, also referred to as reciprocating movement. Owing to the mass inertia, at the reversal point of the oscillating movement a sliding or pushing of the balls may occur on their respective running partners, for example, the machine element itself. As a result, the balls may wear in an undesired manner, thereby causing a quality of the linear guidance to suffer significantly and a service life of the device to be reduced.